There are three different levels in Mt. Moon, populated by oodles of Zubats and plenty battle-hungry trainers. Zubat doesn't stand a chance against Electric attacks (you're probably glad you caught that Pikachu in Viridian Forest, right?), whereas the occasional Geodude is best taken out by a Water attack.

Head north, then wrap around and find the TM09 next to the rock formation. It contains Bullet Seed. Grab it and move north to battle a trainer.

Bug Catcher Kent

Weedle (11)

Kakuna (11)

When the fight concludes, grab the Paralyz Heal nearby. Return to the east and battle the girl next to the sign.

Lass Iris

Clefairy (14)

Head north, then turn right and pass the ladder. Stick to the wall and go southwest to face off with another trainer.

Super Nerd Jovan

Magnemite (11)

Voltorb (11)

Grab the Potion in the corner and continue on east. You will find a Rare Candy in the corner. Don't use it yet. Keep it for much, much later. Fight the Bug Catcher to the left.

Bug Catcher Robby

Caterpie (10)

Metapod (10)

Caterpie (10)

When the battle is over, go east and then north to get the Escape Rope. Go west, then north and turn left to go back to the ladder you passed up initially. It's time to go down. Now follow the narrow tunnel and go up the next ladder at the end. You'll bump into a Team Rocket member.

Team Rocket Grunt

Sandshrew (11)

Rattata (11)

Zubat (11)

After you defeat him, pick up the Star Piece on the small rock plateau and head back to the first floor. Head north from the ladder and wrap around the rock to the left battle Lass.

Lass Miriam

Oddish (11)

Bellsprout (11)

When the battle with Miriam concludes, go southwest. Yep, it's another ladder. Go down to find yet another one and take that one down as well. You battle the second Team Rocket member here.

Team Rocket Grunt

Zubat (11)

Ekans (11)

This room is of course another dead end, but don't leave before you've grabbed TM46 (Thief) from the rock plateau. Notice that small rock over to the right? Examine it to find an Ether, then go back to the first floor. Before you go down the ladder in the northwest corner of Mt. Moon, you have to defeat two more trainers.

Youngster Josh

Rattata (10)

Rattata (10)

Zubat (10)

Hiker Marcos

Geodude (10)

Geodude (10)

Onix (10)

After you beat them, grab the Moon Stone in the northwest corner, then go down the ladder, following yet another linear tunnel to basement level 2. Make a right and go down the stairs to meet the third Team Rocket member.

Team Rocket Grunt

Rattata (13)

Sandshrew (13)

After a quick battle, prepare yourself for a long walk around the rock platform that skirts the central area. As you reach the top, you'll run into another Grunt.

Team Rocket Grunt

Rattata (13)

Zubat (13)

After him, you need to beat another Super Nerd.

Super Nerd Miguel

Grimer (12)

Voltorb (12)

Koffing (12)

Once you're done with his Grimer/Voltorb/Koffing trio, you get to choose one of two fossils.

Should you pick the Dome Fossil or the Helix Fossil? The choice is yours, but here's what the fossils will turn into later in the game:

Dome Fossil: Kabuto (#140) -- which evolves into Kabutops (#141)

Helix Fossil: Omanyte (#138) -- evolves into Omastar (#139)

Both are Rock/Water types. Kabuto has higher Attack and Speed ratings, whereas Omastar has better Defense and Special. It's up to you which one you take, but Kabutops looks a whole lot cooler... Note that you can only get one of the two. You can only get the other one by trading with a friend. Move up and to the left to find a staircase leading to the ladder that goes out. Grab the Antidote near it, then scale the ladders and exit the cave.